Meeting the Many Challenges of Solving the Boltzmann Transport Equation

Karl Rupp
Seminar

Accurate simulation of carrier transport in semiconductor devices requires the solution of the Boltzmann transport equation (BTE), for which a deterministic solution approach based on a spherical harmonics expansion (SHE) is considered. The SHE method leads to a system of partial dierential equations, which is solved numerically using a nite volume scheme. First, recent algorithmic improvements of the SHE method are discussed. Then, the components of the library-centric C++ simulation framework created for the simulation of state-of-the-art semiconductor devices using the SHE method are presented: ViennaGrid provides a exible grid management and allows for dimension-independent programming. ViennaData separates data storage from the grid data structure and allows for associating quantities of arbitrary type with grid elements. ViennaCL provides GPU-accelerated iterative solvers and preconditioners for the solution of the sparse linear systems of equations obtained from the SHE method. The interaction of these free open-source libraries in the device simulator Vienna SHE is outlined. Finally, a brief overview of current and future research activities is given.